Question

From Doppler shifts of the spectral lines in the light coming from the east and west edges of the Sun, astronomers find that the radial velocities of the two edges differ by about 4 km/s, meaning that the Sun’s rotation rate is 2 km/s. Find the approximate period of rotation of the Sun in days. The circumference of a sphere is given by 2πR, where R is the radius of the sphere

Answer 1

To find the approximate period of rotation of the Sun in days, we can use the fact that the Sun's rotation rate is 2 km/s. Using the equation v = 2πR/T, we can solve for the period T. Given that the Sun is located about 26,000 light-years from the center of the Galaxy, we can calculate the circumference of the Sun's orbit as 2πR = 162,920 light-years. Substituting the values into the equation for the period, we find T ≈ 3.5793 ×
`10^7`s.

Step-by-step explanation:

To find the approximate period of rotation of the Sun in days, we can use the fact that the Sun's rotation rate is 2 km/s. We know that the difference in radial velocities of the east and west edges of the Sun is about 4 km/s. Since the Sun rotates in a circular motion, we can equate this difference in velocities to the tangential velocity of an object moving around a circle, which is given by v = 2πR/T (where v is the velocity, R is the radius, and T is the period). From this, we can solve for the period T, which gives us T = 2πR/v. Given that the speed of light is 300,000 km/s and the Sun is located about 26,000 light-years from the center of the Galaxy, we can calculate the circumference of the Sun's orbit as 2πR = 2π(26,000 light-years) = 162,920 light-years. Converting this to kilometers and using the fact that there are approximately 31,536,000 seconds in a year, we find that the circumference of the Sun's orbit is approximately 492,500,000,000 km. Now, we can substitute the values of R and v into the equation for the period to find T ≈ 2π(492,500,000,000 km)/(2 km/s) ≈ 3.0856 ×
`10^{12`. Converting this to days, we have T ≈ 3.5793 ×
`10^7` days.

Answer 2

T= 37 day

Step-by-step explanation:

To solve this exercise we will use the definition of angular velocity as the angular distance, which for a full period is 2pi between time.

w = T / t

The relationship between angular and linear velocity is

v = w r

w = v / r

We substitute everything in the first equation

v / r = 2π / t

t = 2π r / v

Let's reduce to the SI system

V = 2 km / s (1000m / 1km) = 2 10³ m / s

r= R = 6.96 10⁸ m

Let's calculate

t = 2π 6.96 10⁸/2 10³

t = 3.2 10⁶ s

T = t = 3.2 10⁶ s ( 1h/3600s) (1 day/24 h)

T= 37 day